Quantum-mechanical properties of protons in solid molecular hydrogen at megabar pressures

Quantum distributions of protons in three high-pressure phases of solid molecular hydrogen are investigated by the first-principles path integral molecular dynamics (FP-PIMD) method, in which interatomic forces are calculated precisely based on the density functional theory. The distributions have entirely different symmetries from those predicted by conventional simulation with classical treatment of protons. Especially in phase II, we found that molecular rotation is hindered by quantum fluctuation of protons, having a strong resemblance to a quantum distribution of impurity muonium in crystalline silicon. The mechanism of this "quantum localization" is clarified by a detailed study of the potential energy surface for the molecular rotation.